Random walks
From JSXGraph Wiki
Fixed values in this simulation are:
- stepsize [math]\displaystyle{ {}=5 }[/math] and
- Number of steps per walk [math]\displaystyle{ {}= 100 }[/math].
Therefore, the expected squared distance from the starting point will be [math]\displaystyle{ 100\cdot 5^2=2500 }[/math].
Source code
<jsxgraph width="600" height="600">
var brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 300, unitX: 3, unitY: 3});
var t = brd.createElement('turtle');
function run() {
var i,j,dist,sumdist=0.0;
var stepSize = 5;
brd.suspendUpdate();
var nr = $('number').value*1;
for (i=0;i<nr;i++) {
for (j=0;j<100;j++) {
var a = Math.floor(360*Math.random());
t.right(a);
t.forward(stepSize);
}
dist = t.pos[0]*t.pos[0]+t.pos[1]*t.pos[1];
sumdist += dist;
t.home();
}
$('output').value = (sumdist/nr).toFixed(3);
brd.unsuspendUpdate();
}
function clearturtle() {
sumist = 0.0
t.cs();
}
</jsxgraph>
